Various types of games and puzzles have long been known, including among them puzzles in which the pieces can undergo only prescribed motions relative to each other, those pieces being first randomly scrambled and the object then being to solve the puzzle by unscrambling the pieces. In the unscrambled condition, the pieces have a known order. The unscrambling operation requires movement of the puzzle pieces relative to one another; the sequence and types of movements required can vary in degrees of difficulty. In such puzzles, it is also known to make the unscrambling of the puzzle more difficult by necessitating movements of puzzle pieces involving compound actions, as by requiring two pieces to be moved in a co-acting fashion or by causing two degrees of freedom (e.g., piece positions) to be altered by one motion; thus, an involved series of movements may be needed to accomplish what at first glance appears to be a simple transformation. The puzzle pieces may be slid over or around each other, rotated or rearranged by some combination of those motions. For example, there is the familiar "fifteen" puzzle such as shown in U.S. Pat. No. 1,459,937. In that type of puzzle fifteen square puzzle pieces are provided in a frame sixteen units square, leaving just one square empty. The object of the game-puzzle is to arrange the puzzle pieces in a desired pattern through a complicated series of horizontal and vertical shifting movements of the pieces. Another type of puzzle is the so-called Rubik's Cube device marketed by Ideal Toy Company; the same or a similar cube puzzle shown is in U.S. Pat. No. 3,222,072. That puzzle has as its object the rearrangement of the colors on the faces of the pieces through twisting rotations of groups of nine pieces at a time, all such nine pieces being in a particular row or column of the cube.